Chapter 11.2, Problem 7LC

To determine

Find the expressions $\frac{\frac{a}{b}}{c}\text{and}\frac{a}{\frac{b}{c}}$ are equivalent or not.

Answer to Problem 7LC

The expressions $\frac{\frac{a}{b}}{c}\text{and}\frac{a}{\frac{b}{c}}$ are not equivalent.

Explanation of Solution

Given:

The expressions: $\frac{\frac{a}{b}}{c}\text{and}\frac{a}{\frac{b}{c}}$

Concept Used:

Concept Used:

Find the factors of numerator and denominator, and then cancel the common factor and simplify.

For division of rational expression, we always flip the 2^nd expression and put a multiplication sign.

Rule: $\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}·\frac{d}{c}$

Calculation:

  $\frac{\frac{a}{b}}{c}=\frac{a}{b}÷\frac{c}{1}=\frac{a}{b}·\frac{1}{c}=\frac{a}{bc}$

  $\frac{a}{\frac{b}{c}}=\frac{a}{1}÷\frac{b}{c}=\frac{a}{1}·\frac{c}{b}=\frac{ac}{b}$

  $\frac{a}{bc}\ne \frac{ac}{b}$

Thus, the expressions $\frac{\frac{a}{b}}{c}\text{and}\frac{a}{\frac{b}{c}}$ are not equivalent.